{"title":"无界时间尺度上Sturm-Liouville算子解的一些性质","authors":"B. Allahverdiev, H. Tuna","doi":"10.24193/MATHCLUJ.2019.1.01","DOIUrl":null,"url":null,"abstract":"In this article, we investigate the resolvent operator of Sturm-Liouville problem on unbounded time scales. We obtain integral representations for the resolvent of this operator. Later, we discuss some properties of the resolvent operator, such as Hilbert-Schmidt’s kernel property and compactness. Finally, we give a formula for the Titchmarsh-Weyl function of the Sturm-Liouville problem on unbounded time scales. MSC 2010. 34N05, 34L05, 47A10.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Some properties of the resolvent of Sturm-Liouville operators on unbounded time scales\",\"authors\":\"B. Allahverdiev, H. Tuna\",\"doi\":\"10.24193/MATHCLUJ.2019.1.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we investigate the resolvent operator of Sturm-Liouville problem on unbounded time scales. We obtain integral representations for the resolvent of this operator. Later, we discuss some properties of the resolvent operator, such as Hilbert-Schmidt’s kernel property and compactness. Finally, we give a formula for the Titchmarsh-Weyl function of the Sturm-Liouville problem on unbounded time scales. MSC 2010. 34N05, 34L05, 47A10.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/MATHCLUJ.2019.1.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/MATHCLUJ.2019.1.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Some properties of the resolvent of Sturm-Liouville operators on unbounded time scales
In this article, we investigate the resolvent operator of Sturm-Liouville problem on unbounded time scales. We obtain integral representations for the resolvent of this operator. Later, we discuss some properties of the resolvent operator, such as Hilbert-Schmidt’s kernel property and compactness. Finally, we give a formula for the Titchmarsh-Weyl function of the Sturm-Liouville problem on unbounded time scales. MSC 2010. 34N05, 34L05, 47A10.
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